Mandelbrot and Julia Sets of Complex Polynomials Involving Sine and Cosine Functions via Picard-Mann Orbit

被引：3
|
作者：
Hamada, Nuha [1 ]
Kharbat, Faten [1 ]
机构：
[1] Al Ain Univ, Coll Engn, Abu Dhabi, U Arab Emirates
来源：
COMPLEX ANALYSIS AND OPERATOR THEORY | 2023年 / 17卷 / 01期
关键词：
Madelbrot set; Julia set; Fractals; Fixed points; Sine; Cosine; Picard-Mann iteration; Escape criterion;
D O I：
10.1007/s11785-022-01312-w
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The purpose of this paper is to generate fractals of sine and cosine functions for a complex polynomial z(k) + c via Picard-Mann iterations. To generate Mandelbrot and Julia sets, escape criteria are established and proven for sin z(k) + c and cos z(k) + c for Picard-Mann iterations. Various input parameters for different k are used to compare images between sine and cosine. generation time and average number of iterations of the generated Mandelbrot and Julia sets are presented.
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页数：34
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